Approximate Solutions for Nash Differential Games
In this paper, we are concerned with an open-loop Nash differential game. The necessary conditions for an open-loop Nash equilibrium solution are obtained, also the existence for the solution of the dynamical system of the differential game is studied. Picard method is used to find an approximate so...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/7374882 |
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| _version_ | 1832549742055260160 |
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| author | A. A. Megahed A. A. Hemeda H. F. A. Madkour |
| author_facet | A. A. Megahed A. A. Hemeda H. F. A. Madkour |
| author_sort | A. A. Megahed |
| collection | DOAJ |
| description | In this paper, we are concerned with an open-loop Nash differential game. The necessary conditions for an open-loop Nash equilibrium solution are obtained, also the existence for the solution of the dynamical system of the differential game is studied. Picard method is used to find an approximate solution, and the uniform convergence is proved. Finally, we constructed figures for the analysis of the differential game. These results can be applied between economic and financial firms as well as industrial firms. |
| format | Article |
| id | doaj-art-b3fb0dd679f9482aa4dc141f356a1212 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b3fb0dd679f9482aa4dc141f356a12122025-02-03T06:08:39ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/7374882Approximate Solutions for Nash Differential GamesA. A. Megahed0A. A. Hemeda1H. F. A. Madkour2Department of Basic ScienceDepartment of MathematicsDepartment of MathematicsIn this paper, we are concerned with an open-loop Nash differential game. The necessary conditions for an open-loop Nash equilibrium solution are obtained, also the existence for the solution of the dynamical system of the differential game is studied. Picard method is used to find an approximate solution, and the uniform convergence is proved. Finally, we constructed figures for the analysis of the differential game. These results can be applied between economic and financial firms as well as industrial firms.http://dx.doi.org/10.1155/2023/7374882 |
| spellingShingle | A. A. Megahed A. A. Hemeda H. F. A. Madkour Approximate Solutions for Nash Differential Games Journal of Mathematics |
| title | Approximate Solutions for Nash Differential Games |
| title_full | Approximate Solutions for Nash Differential Games |
| title_fullStr | Approximate Solutions for Nash Differential Games |
| title_full_unstemmed | Approximate Solutions for Nash Differential Games |
| title_short | Approximate Solutions for Nash Differential Games |
| title_sort | approximate solutions for nash differential games |
| url | http://dx.doi.org/10.1155/2023/7374882 |
| work_keys_str_mv | AT aamegahed approximatesolutionsfornashdifferentialgames AT aahemeda approximatesolutionsfornashdifferentialgames AT hfamadkour approximatesolutionsfornashdifferentialgames |